Please don't hate me for this

Computer Science Level 5

The base-10 conversion of nevergonnagiveyouup.nevergonnaletyoudown 36 \text{nevergonnagiveyouup.nevergonnaletyoudown}_{36} is equal to A B \dfrac{A}{B} where A A and B B are positive coprime integers. Find the sum of the digits of A + B . A+B.


The answer is 275.

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Trevor B. by Trevor B. , 22, USA

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1 solution

Eek! How can I not hate you for this? 

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x=(Integer('nevergonnagiveyouupnevergonnaletyoudown'.upper(), base=36)/(36^len('nevergonnaletyoudown')))
sum((x.numerator()+x.denominator()).digits())

  • Press Evaluate

By the way, the exact answer is 3228155259133222787454466061098606354383456098128795960696151 13367494538843734067838845976576 \boxed{\frac{3228155259133222787454466061098606354383456098128795960696151}{13367494538843734067838845976576}}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

For those who don't fully understand base conversions check out this simple yet comprehensive post on the topic by a fellow brilliant.org member.

Base Conversions

Cole Coupland - 6 years, 12 months ago

who about the dot? (".") Wouldn't that have no value in base 36?

DPK ­ - 6 years, 10 months ago

Why SageMath when we can do this simply using python? 

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from fractions import Fraction
ns=dict([(chr(i+48),i) for i in range(10)]+[(chr(i),i-87) for i in range(97,123)])
def decfrac(n,b):
    [p,q]=n.split('.')
    return sum(ns[p[-i]]*(b**(i-1)) for i in range(1,len(p)+1))+sum(ns[q[i]]*Fraction(1/Fraction(b**(i+1))) for i in range(0,len(q)))
base=int(input('Enter base = '))
text=input('Enter number in base %d = ' %base) #input must have a decimal point
m=decfrac(text,base)
print('\nExact form:\n\n',m)
print('\nSum of digits of numerator and denominator =',sum(int(i) for i in str(m.numerator+m.denominator)))

Here's the output: 

Enter base = 36
Enter number in base 36 = nevergonnagiveyouup.nevergonnaletyoudown

Exact form:

 3228155259133222787454466061098606354383456098128795960696151/13367494538843734067838845976576

Sum of digits of numerator and denominator = 275

But yeah, the shorter Sage code looks much cooler.

Prasun Biswas - 5 years, 1 month ago

can you please explain me what's wrong with the following code, 

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 from fractions import gcd

\boxed{
 str1='nevergonnagiveyouupnevergonnaletyoudown'

 i=len(str1)-1

 x=0

 c=1

 while(i>=0):

     x+=c*(10+ord(str1[i])-ord('a'))

     c*=36

     i-=1

 p =x

 q=36**20

 hc=gcd(p,q)

 cp=p//hc

 cq=q//hc



 sd=0

 s=cp

 while(s>0):

     sd+=s%10

     s//=10

 s  =cq

 while(s>0):

     sd+=s%10

     s//=10

 print(sd) 
}

Aditya Mishra - 6 years, 8 months ago

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sorry for poor formatting :)

Aditya Mishra - 6 years, 8 months ago

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